Distributed Time Synchronization for Networks with Random Delays and Measurement Noise

In this paper a new distributed asynchronous algorithm is proposed for time synchronization in networks with random communication delays, measurement noise and communication dropouts. Three different types of the drift correction algorithm are introduced, based on different kinds of local time increments. Under nonrestrictive conditions concerning network properties, it is proved that all the algorithm types provide convergence in the mean square sense and with probability one (w.p.1) of the corrected drifts of all the nodes to the same value (consensus). An estimate of the convergence rate of these algorithms is derived. For offset correction, a new algorithm is proposed containing a compensation parameter coping with the influence of random delays and special terms taking care of the influence of both linearly increasing time and drift correction. It is proved that the corrected offsets of all the nodes converge in the mean square sense and w.p.1. An efficient offset correction algorithm based on consensus on local compensation parameters is also proposed. It is shown that the overall time synchronization algorithm can also be implemented as a flooding algorithm ∗Innovation Center, School of Electrical Engineering, University of Belgrade, Serbia, School of Technical Sciences, Singidunum University, Belgrade, Serbia, and the Vlatacom Institute, Belgrade, Serbia (e-mail: [email protected]). †School of Electrical Engineering, University of Belgrade, Serbia and the Vlatacom Institute, Belgrade, Serbia (e-mail: [email protected]). ‡ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology, Stockholm, Sweden (e-mail: [email protected]). This work was supported by the EU Marie Curie CIG (PCIG12-GA-2012-334098), Knut and Alice Wallenberg Foundation, the Swedish Strategic Research Foundation and the Swedish Research Council. 1 ar X iv :1 70 5. 10 40 8v 2 [ cs .S Y ] 2 F eb 2 01 8 with one reference node. It is proved that it is possible to achieve bounded error between local corrected clocks in the mean square sense and w.p.1. Simulation results provide an additional practical insight into the algorithm properties and show its advantage over the existing methods.